Shape ambiguities in structure from motion
Lecture notes in computer sciencePublished 1 January 1996
Richard Szeliski, Sing Bing Kang
Citations15
SJR quartileQ2
SJR score0.35
SNIP0.55
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
Abstract
This paper examines the fundamental ambiguities and uncertainties inherent in recovering structure from motion. By examining the eigenvectors associated with null or small eigenvalues of the Hessian matrix, we can quantify the exact nature of these ambiguities and predict how they will affect the accuracy of the reconstructed shape. Our results for orthographic cameras show that the bas-relief ambiguity is significant even with many images, unless a large amount of rotation is present. Similar results for perspective cameras suggest that three or more frames and a large amount of rotation are required for metrically accurate reconstruction.
Keywords
Computer ScienceEngineering
Choice Reviews OnlineNumerical recipes in C: the art of scientific computing
17,989 Citations1993Press, William H, Flannery, Brian P +2 more
International Journal of Computer VisionShape and motion from image streams under orthography: a factorization method
2,884 Citations1992Carlo Tomasi, Takeo Kanade
A factorization method is developed that can overcome the difficulty by recovering shape and motion under orthography without computing depth as an intermediate step, and gives accurate results.
Mathematica: A System for Doing Mathematics by Computer
2,804 Citations1988Stephen Wolfram
This new edition maintains the format of the original book and is the single most important user guide and reference for Mathematica--all users ofMathematica will need this edition.
NatureA computer algorithm for reconstructing a scene from two projections
2,364 Citations1981H. C. Longuet–Higgins
A simple algorithm for computing the three-dimensional structure of a scene from a correlated pair of perspective projections is described here, when the spatial relationship between the two projections is unknown.
Mathematics of ComputationNumerical Methods in Finite Element Analysis.
2,045 Citations1977Lars B. Wahlbin, Klaus‐Jürgen Bathe +1 more
Numerical methods in finite element analysis, Numerical techniques in finite elements analysis, and so on.
Lecture notes in computer scienceMathematica: A system for doing mathematics by computer?
1,214 Citations2005Bruno Buchberger
The title of the talk coincides with the title of Stephen Wolfram's book on his Mathematica system except that in the titleof the talk there is a question mark.
Journal of the Optical Society of America AAffine structure from motion
875 Citations1991Jan J. Koenderink, Andrea J. van Doorn
It is indicated how solutions of the structure-from-motion problem can be stratified in such a way that one explicitly knows at which stages various a priori assumptions enter and specific geometrical expertise is required.
Lecture notes in computer scienceWhat can be seen in three dimensions with an uncalibrated stereo rig?
833 Citations1992Olivier Faugeras
This paper addresses the problem of determining the kind of three- dimensional reconstructions that can be obtained from a binocular stereo rig for which no three-dimensional metric calibration data is available, and shows that even in this case some very rich non-metric reconstructions of the environment can nonetheless be obtained.
IEEE Transactions on Pattern Analysis and Machine IntelligenceUniqueness and Estimation of Three-Dimensional Motion Parameters of Rigid Objects with Curved Surfaces
827 Citations1984R. Tsai, Thomas S. Huang
It is shown that seven point correspondences are sufficient to uniquely determine from two perspective views the three-dimensional motion parameters (within a scale factor for the translations) of a rigid object with curved surfaces.
IEEE Journal on Robotics and AutomationError modeling in stereo navigation
501 Citations1987Larry Matthies, Steven A. Shafer
Simulations show that, compared to scalar error models, the 3D Gaussian reduces the variance in robot position estimates and better distinguishes rotational from translational motion.
IEEE Transactions on Pattern Analysis and Machine IntelligenceRecursive estimation of motion, structure, and focal length
483 Citations1995A. Azarbayejani, Alex Pentland
Presents a formulation for recursive recovery of motion, pointwise structure, and focal length from feature correspondences tracked through an image sequence, yielding a stable and accurate estimation framework which applies uniformly to both true perspective and orthographic projection.
Stereo from uncalibrated cameras
432 Citations2003Richard Hartley, Rajiv Gupta +1 more
The problem of computing placement of points in 3-D space, given two uncalibrated perspective views, is considered and it is possible to determine projective invariants of3-D geometric configurations from two perspective views.
Journal of Visual Communication and Image RepresentationRecovering 3D Shape and Motion from Image Streams Using Nonlinear Least Squares
327 Citations1994Richard Szeliski, Sing Bing Kang
A shape and motion estimation algorithm based on nonlinear least squares applied to the tracks of features through time is presented, using an object-centered representation for faster and more accurate structure and motion recovery.
Springer series in information sciencesTheory of Reconstruction from Image Motion
318 Citations1993Stephen J. Maybank
Theory of Reconstruction from Image Motion presents the mathematics underlying the reconstruction of camera motion from the movements of points in the camera image, employing mathematical methods drawn from linear algebra, projective geometry, algebraic geometry, the theory of transversality and the theories of least squares approximation.
International Journal of Computer VisionRelative orientation
291 Citations1990Berthold K. P. Horn
A simple iterative scheme for recovering relative orientation that does not require a good initial guess for the baseline and the rotation, and is well known that at least five pairs of rays are needed.
IEEE Transactions on Pattern Analysis and Machine IntelligenceInherent ambiguities in recovering 3-D motion and structure from a noisy flow field
271 Citations1989Gilad Adiv
Two problems which may arise due to the presence of noise in the flow field are examined and constraints and parameters which can be recovered even in ambiguous situations are presented.
IEEE Transactions on Pattern Analysis and Machine IntelligenceOptimal motion and structure estimation
268 Citations1993Juyang Weng, Narendra Ahuja +1 more
MIT Press eBooksArtificial Vision for Mobile Robots: Stereo Vision and Multisensory Perception
212 Citations1991Nicholas Ayache, Peter Sander
Artificial Vision for Mobile Robots "presents new theoretical and practical tools useful for providing mobile robots with artificial vision in three dimensions, including passive binocular and trinocular stereo vision, local and global 3D map reconstructions, fusion of local 3D maps into a global3D map, 3D navigation, control of uncertainty, and strategies of perception".
Relative 3-D reconstruction using multiple uncalibrated images
123 Citations2002Roger Mohr, F. Veillon +1 more
Computing matched-epipolar projections
91 Citations2002Richard Hartley, Rajiv Gupta
A new method for image rectification, the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of matched epipolar projections, based on an examination of the essential matrix of Longuet-Higgins (1981), which describes the epipolar geometry of the image pair.
IEEE Transactions on Pattern Analysis and Machine IntelligenceStatistical analysis of inherent ambiguities in recovering 3-D motion from a noisy flow field
80 Citations1992G. S. Young, Rama Chellappa
Recursive estimation of structure and motion using relative orientation constraints
73 Citations2002A. Azarbayejani, B. Horowitz +1 more
A recursive estimation technique for recovering the 3-D motion and pointwise structure of an object is presented which is remarkably accurate, stable, and fast-conveying.
Projective depth: A geometric invariant for 3D reconstruction from two perspective/orthographic views and for visual recognition
69 Citations2002Amnon Shashua
It is shown that with the correspondences coming from four non-coplanar points in the scene and the corresponding epipoles, it is possible to define and reconstruct a projective invariant that can be used later to reconstruct the projective or affine structure of the scene or directly to generate novel views of thescene.
Recursive motion and structure estimation with complete error characterization
51 Citations2002Stefano Soatto, Pietro Perona +2 more
An algorithm that performs recursive estimation of ego-motion and ambient structure from a stream of monocular perspective images of a number of feature points is presented, based on an extended Kalman filter that integrates over time the instantaneous motion and structure measurements computed by a two-perspective-views step.
Image and Vision ComputingAnalytical results on error sensitivity of motion estimation from two views
43 Citations1990Konstantinos Daniilidis, Hans-Hellmut Nagel
This paper proposes a norm possessing a reasonable geometric interpretation in the image plane and shows by analytical means that a simplification of this norm leading to a closed form solution has undesirable properties.
Optimal motion estimation
42 Citations2003Minas E. Spetsakis, John Aloimonos
It is shown that some of the difficulties inherent in the two-frame approach disappear when redundancy in the data is introduced, and the authors present two efficient ways to approximate the problem.
Structure and motion in two dimensions from multiple images: a least squares approach
37 Citations2002C. James Taylor, David Kriegman +1 more
A nonlinear optimization algorithm for the estimation of structure and motion parameters
36 Citations2003R.V. Raja Kumar, Arun P. Tirumalai +1 more
A nonlinear least-squares optimization technique is proposed which uses the Levenberg-Marquardt method and estimates the motion and structure parameters to a global scale factor by minimizing an objective function.
Extended structure and motion analysis from monocular image sequences
34 Citations2002Ning Cui, John Weng +1 more
The simulations and experiments with long image sequences of real world scenes indicate that the optimization method developed greatly reduces the computational complexity and substantially improves the motion and structure estimation over that produced by linear algorithms.
Incorporating motion error in multi-frame structure from motion
32 Citations2002J. Oliensis, Joseph Thomas
A method for recursively recovering structure from motion that can deal with motion error and introduce large, correlated errors in the structure estimate is proposed.
Structure and motion from line segments in multiple images
20 Citations2003C. James Taylor, David Kriegman
The approach can be directly used for accurately locating correspondences in multieyed stereo, as well as for pose estimation from landmarks, and its effectiveness is demonstrated quantitatively through simulation and qualitatively with a real image sequence.
Understanding noise: The critical role of motion error in scene reconstruction
20 Citations2002Joseph Thomas, Andrew J. Hanson +1 more
The authors attempt to isolate the effect of the motion error as correlations in the structure error and show theoretically that these correlations can improve existing multi-frame structure from motion techniques.
Vision ResearchVisual motion ambiguity
16 Citations1986H. C. Longuet–Higgins
This paper discusses a number of points that arise in the visual interpretation of optic flow fields and particular attention is given to the case in which a flow field is visually ambiguous.
A direct data approximation based motion estimation algorithm
12 Citations2002C. Debrunner, Narendra Ahuja
A novel algorithm for estimating motion and structure from orthographic projections is presented, based on the image locations of a set of points on a rigid object viewed in many frames, with accurate results from synthetic data given the positions of 10 points over 10 frames.